Research On Dominance-based Rough Set Approach And Its Extensions

Dominance-based rough set approach takes users' preferences into consideration for reasoning about ordinal data,which distinguishes itself from other extensions of the rough set theory.Therefore,it can discover and process inconsistencies coming from consideration of criteria,that is,attributes with preference-ordered domains,such as test scores,product quality and debt ratio.This theory has greatly promoted the research of multi-criteria decision making problems involving preferential information.This thesis is mainly devoted to the study of dominance-based rough set approach and its extensions to more complex systems and with other theories.The most concern for this thesis is attribute reduction for ordered decision systems.In Chapter 3,we consider the discernibility matrix based attribute reduction for an ordered decision system.First,the discernibility matrix is constructed to perform attribute reduction for an ordered decision system.Second,in order to reduce the com-putational complexity,only minimal elements are located in the discernibility matrix.Then,an algorithm is proposed to find all minimal elements which are determined by particular sample pairs and are characterized via relative discernibility relations.In Chapter 4,based on the greedy hill climbing method,heuristic attribute re-duction algorithms are proposed to deal with ordered decision systems.Unfortunately,they are often time-consuming,especially when applied to deal with large scale data sets with high dimensions.To reduce the complexity,a novel accelerator is introduced in heuristic algorithms from the perspectives of objects and criteria.Based on the new accelerator,the size of the system is lessened thus making the accelerated algorithms faster than their original counterparts while maintaining the same reducts.Dempster-Shafer theory of evidence is also an approach to modeling and manip-ulating uncertain information.In Chapter 5,we investigate the problem of attribute reduction for ordered decision systems based on evidence theory.Belief and plausibil-ity functions are employed to define relative belief and plausibility reducts of ordered decision systems.Relationships among various types of relative reducts are thoroughly studied in ordered decision systems.The inner and outer significance measures of a criterion are presented to search for a relative belief/plausibility reduct.Chapter 6 mainly deals with approaches to attribute reduction in incomplete or-dered information systems in which some attribute values may be lost or absent.By introducing a new kind of dominance relation,named the characteristic-based domi-nance relation,to incomplete ordered information systems,we expand the potential applications of dominance-based rough set approach.An approach on the basis of the discernibility matrix and the discernibility function to computing all(relative)reducts is investigated in incomplete ordered information systems(consistent incomplete or-dered decision tables).To reduce the computational burden,a heuristic algorithm with polynomial time complexity for finding a single(relative)reduct is designed by using the inner and outer significance measures of each criterion candidate.In Chapter 7,approximate distribution reducts are proposed in inconsistent interval-valued ordered decision systems,where the order relation is the well known K-M order.We present a theoretical method based on the discernibility matrix to enumerate all reducts and a practical approach on the basis of significance to find one reduct.And two equivalent definitions of approximate distribution reducts are also introduced.In Chapter 8,our attention is paid to ordered fuzzy decision systems,where decision classes are ordered and fuzzy.First,the dominance-based rough fuzzy approximations of an upward or downward cumulated fuzzy set are introduced.Second,lower and upper reducts relative to a certain cumulated fuzzy set are proposed to eliminate re-dundant criteria.Then,two approaches to attribute reduction are presented based on the discernibility matrix and the heuristic strategy,respectively.Also,decision rules are extracted directly from these approximations and some applicable and simplified de-cision rules are obtained according to requirements of decision makers.Finally,a case study in bankruptcy risk analysis is used to illustrate the mechanism of the proposed methods.